MA 318: Combinatorics

Credits: 3:0

Pre-requisites :

1. Calculus, Linear algebra and some exposure to proofs and abstract mathematics.
2. Programming in Sage will be a part of every lecture. Students will need to bring a laptop with access to the IISc WLAN.

Counting problems in sets, multisets, permutations, partitions, trees, tableaux; ordinary and exponential generating functions; posets and principle of inclusion-exclusion, the transfer matrix method; the exponential formula, Polya theory; bijections, combinatorial identities and the WZ method.

Suggested books and references:

1. Herbert Wilf, Generatingfunctionology, ISBN-13 - 978-1568812793; Freely downloadable from http://www.math.upenn.edu/~wilf/DownldGF.html.
2. Richard P. Stanley, Enumerative Combinatorics: Volume 1 (Second Edition), ISBN-13 - 978-1107602625 Older version freely downloadable from http://www-math.mit.edu/~rstan/ec/ec1/.

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